Non-negative sparse coding
Patrik O. Hoyer
- 07 Nov 2002
- pp 557-565
TL;DR: A simple yet efficient multiplicative algorithm for finding the optimal values of the hidden components of non-negative sparse coding and how the basis vectors can be learned from the observed data is shown.
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Abstract: Non-negative sparse coding is a method for decomposing multivariate data into non-negative sparse components. We briefly describe the motivation behind this type of data representation and its relation to standard sparse coding and non-negative matrix factorization. We then give a simple yet efficient multiplicative algorithm for finding the optimal values of the hidden components. In addition, we show how the basis vectors can be learned from the observed data. Simulations demonstrate the effectiveness of the proposed method.
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Citations
Non-negative Matrix Factorization with Sparseness Constraints
TL;DR: In this paper, the notion of sparseness is incorporated into NMF to improve the found decompositions, and the authors provide complete MATLAB code both for standard NMF and for their extension.
Online Learning for Matrix Factorization and Sparse Coding
TL;DR: In this paper, a new online optimization algorithm based on stochastic approximations is proposed to solve the large-scale matrix factorization problem, which scales up gracefully to large data sets with millions of training samples.
Graph Regularized Nonnegative Matrix Factorization for Data Representation
TL;DR: In GNMF, an affinity graph is constructed to encode the geometrical information and a matrix factorization is sought, which respects the graph structure, and the empirical study shows encouraging results of the proposed algorithm in comparison to the state-of-the-art algorithms on real-world problems.
Document clustering based on non-negative matrix factorization
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TL;DR: This paper proposes a novel document clustering method based on the non-negative factorization of the term-document matrix of the given document corpus that surpasses the latent semantic indexing and the spectral clustering methods not only in the easy and reliable derivation of document clustered results, but also in document clusters accuracies.
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Projected Gradient Methods for Nonnegative Matrix Factorization
TL;DR: This letter proposes two projected gradient methods for nonnegative matrix factorization, both of which exhibit strong optimization properties and discuss efficient implementations and demonstrate that one of the proposed methods converges faster than the popular multiplicative update approach.
References
Learning the parts of objects by non-negative matrix factorization
TL;DR: An algorithm for non-negative matrix factorization is demonstrated that is able to learn parts of faces and semantic features of text and is in contrast to other methods that learn holistic, not parts-based, representations.
14.2K
Learning parts of objects by non-negative matrix factorization
D. D. Lee
- 01 Jan 1999
TL;DR: In this article, non-negative matrix factorization is used to learn parts of faces and semantic features of text, which is in contrast to principal components analysis and vector quantization that learn holistic, not parts-based, representations.
9.6K
•Proceedings Article
Algorithms for Non-negative Matrix Factorization
Daniel D. Lee,H. Sebastian Seung +1 more
- 01 Jan 2000
TL;DR: Two different multiplicative algorithms for non-negative matrix factorization are analyzed and one algorithm can be shown to minimize the conventional least squares error while the other minimizes the generalized Kullback-Leibler divergence.
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Independent Component Analysis
Aapo Hyvärinen,Juha Karhunen,Erkki Oja +2 more
- 18 May 2001
TL;DR: Independent component analysis as mentioned in this paper is a statistical generative model based on sparse coding, which is basically a proper probabilistic formulation of the ideas underpinning sparse coding and can be interpreted as providing a Bayesian prior.
Emergence of simple-cell receptive field properties by learning a sparse code for natural images
TL;DR: It is shown that a learning algorithm that attempts to find sparse linear codes for natural scenes will develop a complete family of localized, oriented, bandpass receptive fields, similar to those found in the primary visual cortex.